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与给定模型相容的推断之存在性AI 解读

4 If ${p_{\theta}$ is a $\sigma$-additive statistical model and $\pi$ a finitely additive prior, then any statistic T is sufficient, with respect to a suitable inference consistent with ${p_{\theta}$ and $\pi$, provided only that $p_{\theta}(T = t) = 0$ for all $\theta$ and t. Here, sufficiency is to be intended in the Bayesian sense, and consistency in the sense of Lane and Sudderth. As a corollary, if ${p_{\theta}$ is $\sigma$-additive and diffuse, then, whatever the prior $…

非线性回归中贝叶斯 c 与 D 最优设计札记AI 解读

We present a version of Elfving's theorem for the Bayesian D-optimality criterion in nonlinear regression models. The Bayesian optimal design can be characterized as a design which allows a representation of a (uniquely determined) boundary point of a convex subset of $L^2$-integrable functions. A similar characterization is given for the Bayesian c-optimality criterion where a (possible) nonlinear function of the unknown parameters has to be estimated. The results are…

层次先验的选择：正态均值估计的可容许性AI 解读

In hierarchical Bayesian modeling of normal means, it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters (e.g., variances and highest-level means). This common practice often results in an inadequate overall prior, inadequate in the sense that estimators resulting from its use can be inadmissible under quadratic loss. In this paper, hierarchical priors for normal means are categorized in terms of admissibility and…

通过序贯插补实现非参数分层贝叶斯估计AI 解读

We consider the empirical Bayes estimation of a distribution using binary data via the Dirichlet process. Let $\mathscr{D}(\alpha)$ denote a Dirichlet process with $\alpha$ being a finite measure on Instead of having direct samples from an unknown random distribution F from $\mathscr{D}(\alpha)$, we assume that only indirect binomial data are observable. This paper presents a new interpretation of Lo's formula, and thereby relates the predictive density of the observations…

马尔可夫链蒙特卡洛收敛诊断：比较综述AI 解读

A critical issue for users of Markov chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic…

似然函数与似然原则的推广AI 解读

The parametric likelihood and likelihood principle (LP) play a central role in parametric methodology and in the foundations of statistics. The main purpose of this article is to extend the concepts of likelihood and LP to general inferential aims and models covering, for example, prediction and empirical Bayes models. The likelihood function is the joint distribution of the data and the unobserved variables of inferential interest, considered as a function of the parameters…

贝叶斯序贯两阶段抽样AI 解读

We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a…

推断对先验边际分布的局部敏感性AI 解读

The sensitivity of posterior expectations to perturbations of prior marginals is investigated, using a local method. This approach is particularly well suited to high-dimensional parameter spaces. Qualitative and quantitative results are obtained regarding the propagation of sensitivity in multiparameter settings. More specifically, a posterior expectation is treated as a functional of the prior marginal. The derivative of this functional is evaluated at the nominal prior…

方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

如何成为更好的贝叶斯统计学家AI 解读

Consider an experiment yielding an observable random quantity X whose distribution is indexed by a real parameter ø. Suppose that a statistician is prepared to execute a Bayes procedure in estimating ø and has quantified available prior information about ø in his chosen prior distribution G. Suppose that before this estimation process is completed, the statistician becomes aware of the outcome Y of a “similar” experiment. In this article we investigate the questions of…

合并似然的经验贝叶斯方法AI 解读

Suppose that several independent experiments are observed, each one yielding a likelihood L k (θ k ) for a real-valued parameter of interest θ k . For example, θ k might be the log-odds ratio for a 2 × 2 table relating to the kth population in a series of medical experiments. This article concerns the following empirical Bayes question: How can we combine all of the likelihoods L k to get an interval estimate for any one of the θ k 's, say θ1? The results are presented in…

贝叶斯序贯两阶段抽样AI 解读

We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a…

方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

合并似然的经验贝叶斯方法AI 解读

Suppose that several independent experiments are observed, each one yielding a likelihood L k (θ k ) for a real-valued parameter of interest θ k . For example, θ k might be the log-odds ratio for a 2 × 2 table relating to the kth population in a series of medical experiments. This article concerns the following empirical Bayes question: How can we combine all of the likelihoods L k to get an interval estimate for any one of the θ k 's, say θ1? The results are presented in…

摘要暂缺

A two-way multivariate normal model is proposed and attention is focused on estimation of the mean values when the common variance of the observations is unknown. A class of empirical Bayes estimators is proposed and mean-squared errors are given. A lower bound on the mean-squared error is found and related to risk asymptotics. A James-Stein-type estimator is derived and compared with its competitor--a modal estimator that is obtained from a hierarchical prior for the…

摘要暂缺

二参数指数族中后验分位数的频率学有效性AI 解读

Berger & Bernardo's (1989) reference priors and Tibshirani (1989) priors are derived for distributions in Bar-Lev & Reiser's (1982) two-parameter exponential family when either the location or the scale parameter is of interest. The reference prior is shown to be a Tibshirani prior. Furthermore, conditions under which a Tibshirani prior is a higher-order matching prior are investigated. When both the parameters are of interest, it is also shown that the reference prior…

贝叶斯设计问题的预测方法及其在正态回归模型中的应用AI 解读

A predictive decision-theoretic approach is developed for the Bayesian design problem. The loss functions used are fair Bayes, or proper scoring rules, and are quadratic measures of distance between probability measures. Optimal Bayesian designs are those which minimise the preposterior risk for the decision problem. Such designs typically depend on both the prior distribution and the loss function. The results are applied to certain normal regression models where explicit…

利用多元正态混合进行贝叶斯曲线拟合AI 解读

Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multidimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to generalised kernel regression estimates, but the…

面向多重假设检验的贝叶斯实验设计AI 解读

The problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests is considered. The Bayesian decision theoretic approach is used to arrive at several new optimality criteria for this purpose. For a single hypothesis test, the resulting optimal designs are the well-known φ-optimal designs that minimize the posterior variance of the parameter being tested. For multiple tests, an experimental design must perform well under several…

利用耦合样本路径研究 MCMC 算法的收敛AI 解读

I describe a simple procedure for investigating the convergence properties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same sequence of random deviates for each run. By examining the distribution of the iteration at which all sample paths couple, convergence properties for the system can be established. The procedure also provides a simple diagnostic for detecting modes in multimodal posteriors.…

半参数二元回归的贝叶斯推断AI 解读

We propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale. Predictors enter linearly. We demonstrate Bayesian inference calculations in this model. By modifying the Dirichlet process, we obtain a natural prior measure over this semiparametric model, and we use Polya sequence theory to formulate this measure in terms of a finite number of unobserved variables. We design a…

多评分者有序数据的贝叶斯分析：自动作文评分应用AI 解读

A framework is proposed for the analysis of ordinal categorical data when ratings from several judges are available. I emphasize the tasks of estimating latent trait characteristics of individual items, regressing these latent traits on observed covariates, and comparing the performance of raters. The model is illustrated in the design and evaluation of an automated essay grader. This grader is based on a regression of variables, obtained from a grammar checker, on essay…